The Winston Company has four distribution centers (A, B, C, and D) that require 40,000, 60,000, 30,000, and 50,000 gallons of de-ionized water, respectively, per month for cleaning their long-haul trucks. Three de-ionized water wholesalers (1, 2, and 3) indicated their willingness to supply as many as 50,000, 70,000, and 60,000 gallons, respectively. The total cost (shipping plus price) of delivering 1,000 gallons of de-ionized water from each wholesaler to each distribution center is shown in the following table: Distribution Center B C Wholesaler A D 1 $1.70 $1.90 $1.60 $1.70 2 $1.90 $1.60 $1.70 $1.40 $1.60 3 $1.50 $1.80 $1.40 a. Which of the following statements regarding setting up the tableau for the optimal solution for this problem is true? OA. The sum of supply capacities is greater than the sum of demands, so a dummy distribution center is needed. OB. The sum of supply capacities is less than the sum of demands, so a dummy wholesaler is needed. C. The sum of supply capacities equals the sum of demands, so no dummy wholesaler or distribution center is needed. The capacity is fully utilized and the demand is fully satisfied. b. What is the total cost of the solution? The optimal cost is $. (Enter your response rounded to the nearest dollar.)

The Winston Company has four distribution centers (A, B, C, and D) that require 40,000, 60,000, 30,000, and 50,000 gallons of de-ionized water, respectively, per month for cleaning their long-haul trucks. Three de-ionized water wholesalers (1, 2, and 3) indicated their willingness to supply as many as 50,000, 70,000, and 60,000 gallons, respectively. The total cost (shipping plus price) of delivering 1,000 gallons of de-ionized water from each wholesaler to each distribution center is shown in the following table: Distribution Center B C Wholesaler A D 1 $1.70 $1.90 $1.60 $1.70 2 $1.90 $1.60 $1.70 $1.40 $1.60 3 $1.50 $1.80 $1.40 a. Which of the following statements regarding setting up the tableau for the optimal solution for this problem is true? OA. The sum of supply capacities is greater than the sum of demands, so a dummy distribution center is needed. OB. The sum of supply capacities is less than the sum of demands, so a dummy wholesaler is needed. C. The sum of supply capacities equals the sum of demands, so no dummy wholesaler or distribution center is needed. The capacity is fully utilized and the demand is fully satisfied. b. What is the total cost of the solution? The optimal cost is $. (Enter your response rounded to the nearest dollar.)

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 2C

See similar textbooks

Similar questions

The Winston Company has four distribution centers (A, B, C, and D) that require 40,000, 60,000, 30,000, and 50,000 gallons of de-ionized water, respectively, per month for cleaning its long-haul trucks. Three de-ionized water wholesalers (1, 2, and 3) indicated their willingness to supply as many as 50,000, 70,000, and 60,000 gallons, respectively. The total cost (shipping plus price) of delivering 1,000 gallons of de-ionized water from each wholesaler to each distribution center is shown in the following table: Distribution Center Wholesaler A B C D 1 $1.30 $1.40 $1.80 $1.60 2 $1.30 $1.50 $1.80 $1.60 3 $1.60 $1.40 $1.70 $1.50 Determine the optimal solution. Show that all capacities have been exhausted and that all demands can be met with this solution. (use below table format, numbers are generic, erase them) Distribution Center Supply Wholesaler A B C D 1 xx xx x x 400-200-150-50=0 2…
The Winston Company has four distribution centers (A, B, C, and D) that require 40,000, 60,000, 30,000, and 50,000 gallons of de-ionized water, respectively, per month for cleaning their long-haul trucks. Three de-ionized water wholesalers (1, 2, and 3) indicated their willingness to supply as many as 50,000, 70,000, and 60,000 gallons, respectively. The total cost (shipping plus price) of delivering 1,000 gallons of de-ionized water from each wholesaler to each distribution center is shown in the following table: Distribution Center Wholesaler A B C D 1 $1.30 $1.40 $1.80 $1.60 2 $1.30 $1.50 $1.80 $1.60 3 $1.60 $1.40 $1.70 $1.50 a. Determine the optimal solution. Show that all capacities have been exhausted and that all demands can be met with this solution. b. What is the total cost of the solution?
PharmaCo wants to determine how to deploy sales representatives across its Western U.S. region to support a new drug for obesity. Sales representatives will be located in a "home city", which they serve, in addition to cities with feasible commuting distance, with the objective that all cities must be served by at least one sales representative. The feasible connections between each city in the region are listed below (1 indicates a feasible connection, potential home cities are shown in columns, and cities served in rows): Potential Rep Home City Served? Albuquerque El Paso Denver Phoenix San Diego Los Angeles San Francisco Portland Seattle Las Vegas Salt Lake City Albuquerque 1 1 1 1 0 0 0 0 0 0 0 El Paso 1 1 0 1 0 0 0 0 0 0 0 Denver 1 0 1 1 0 0 0 0 0 0 1 Phoenix 1 1 1 1 1 1 0 0 0 1 1 San Diego 0 0 0 1 1 1 1 0 0 1 0…
PharmaCo wants to determine how to deploy sales representatives across its Western U.S. region to support a new drug for obesity. Sales representatives will be located in a "home city", which they serve, in addition to cities with feasible commuting distance, with the objective that all cities must be served by at least one sales representative. The feasible connections between each city in the region are listed below (1 indicates a feasible connection, potential home cities are shown in columns, and cities served in rows): Potential Rep Home City Served? Albuquerque El Paso Denver Phoenix San Diego Los Angeles San Francisco Portland Seattle Las Vegas Salt Lake City Albuquerque 1 1 1 1 0 0 0 0 0 0 0 El Paso 1 1 0 1 0 0 0 0 0 0 0 Denver 1 0 1 1 0 0 0 0 0 0 1 Phoenix 1 1 1 1 1 1 0 0 0 1 1 San Diego 0 0 0 1 1 1 1 0 0 1 0…
Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice. What is the objective function? Group of answer choices Max Z = $3AD + $3AE + $4BD + $3BE + $5CD + $3CE + $4DF + $4DG + $4DH + $10EF + $9EG + $8EH Min Z = $3AD + $3AE + $4BD + $3BE + $5CD + $3CE + $4DF + $4DG + $4DH + $10EF + $9EG + $8EH Min Z = $3AD + $3BE + $5CD + $3CE…
Obtain the initial basic feasible solution to the following transportation problem using north- west corner rule D1 D2 D3 D4 SUPPLY O1 6 4 1 5 14 O2 8 9 2 7 16 O3 4 3 6 2 5 DEMAND 6 10 15 4 Where O1, O2, O3, O4 are the origins and D1, D2, D3, D4 are requirements respectively. Obtain the minimum cost and comment upon the concept of transportation problem and its significance in detail.
A logistics company plans to provide coal logistics transportation services to HY coal sales enterprise. HY coal sales enterprise has coal storage and sales points in B and D, with available coal quantities of 1600t and 8000t, respectively; A and C represents the locations of two coal users, with a demand of 8000t and 1600t respectively. The distribution of relevant locations and travel distances are shown in Figure 1. Based on the above conditions, try to calculate and explain from the perspective of transportation capacity consumption: How should logistics company HY plan transportation routes in order to make them more reasonable? (a transportation route planning scheme needs to be illustrated) . Note:The solution should not be hand written.
The Winston Company has four distribution centers(A, B, C, and D) that require 40,000, 60,000, 30,000, and 50,000 gallons of de-ionized water, respectively,per month for cleaning their long-haul trucks. Threede-ionized water wholesalers (1, 2, and 3) indicatedtheir willingness to supply as many as 50,000, 70,000,and 60,000 gallons, respectively. The total cost (ship-ping plus price) of delivering 1,000 gallons of de-ionizedwater from each wholesaler to each distribution center isshown in the following table: a. Determine the optimal solution. Show that all capacitieshave been exhausted and that all demands can be metwith this solution.b. What is the total cost of the solution?
In a transshipment problem involving 3 origins, 2 intermediate points, and 4 final destinations, what is the maximum number of decision variables?
Santa Cruz Bottling is a manufacturer of organic soft drinks on the coast of central California. Its products are enjoying a growing reputation and increased demand throughout the American Southwest. Because of the high cost of transportation soft drinks, they are considering a new plant to serve the states of New Mexico and Arizona. A key concern in their search for a new location is the resultant transportation cost to serve their key markets. Following is a list of cities where their main wholesale customers are located, along with estimated annual demand in cased of product for each. CITY x-COORDINATES y-COORDINATES # OF CASES Phoenix 281 281 24,500 Tucson 381 156 20,000 Albuquerque 831 481 28,000 Santa Fe 881…
A farmers' cooperative association plans to build a new sugar mill in Georgetown. Theprimary objective of the mill is to provide the farmers with a place to take their crop forprocessing that will reduce their transportation costs. The members of the co-op believe thatthe center-of-gravity method is appropriate for this objective. While there are over 200 sugarcane farms in the region, they are tightly clustered around six villages. Using the data below,use the center-of-gravity method to calculate the coordinates of the best location for this mill.All mileage references use Browns Town as (0,0).VillageMiles East ofBrowns TownMiles North ofBrowns TownSugar CanetonnageBarney Valley 90 10 240,000Blue Pasture 140 60 320,000Congo Valley 20 70 450,000Bower 50 20 120,000Rabacca 100 80 60,000Salem 10 120 140,000
Mr. Felix Cross, is a well-known and successful businessman who is involved in a variety of business ventures in Saint Lucia. One of those ventures is the largest coconut plantation in Saint Lucia, located in the Roseau Valley on the West Coast. Between the years 2012 to 2018 the plantation experienced a year-on-year increase in profitability as it had progressively become the largest supplier of coconuts to the many small businesses that plied their trade as road-side coconut water vendors. From late 2018 through to 2019, Mr. Cross noticed a progressive decline in the volume of coconuts being purchased from his plantation as an increasing number of regulations and restrictions were being placed upon the vendors, with regards to the locations they were allowed to trade. Though the coconut plantation business was still profitable, demand had dropped off to a point where only 60% of the nuts being harvested were being sold on to vendors. The remaining nuts were laid to waste. It became…